A left topological monoid associated to a topological groupoid

This paper presents a fanctor \(S\) from the category of groupoids to the category of semigroups. Indeed, a monoid \(S_G\) with a right zero element is related to a topological groupoid \(G\). The monoid \(S_G\) is a subset of \(C(G,G)\), the set of all continuous functions from \(G\) to \(G\), and...

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Bibliographic Details
Published in:arXiv.org 2013-11
Main Author: Amiri, Habib
Format: Article
Language:English
Subjects:
Chemical industry
Continuity (mathematics)
Linear operators
Monoids
Operators (mathematics)
Subgroups
Topology
Online Access:Get full text
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Summary:This paper presents a fanctor \(S\) from the category of groupoids to the category of semigroups. Indeed, a monoid \(S_G\) with a right zero element is related to a topological groupoid \(G\). The monoid \(S_G\) is a subset of \(C(G,G)\), the set of all continuous functions from \(G\) to \(G\), and with the compact- open topology inherited from C(G,G) is a left topological monoid. The group of units of \(S_G\), which is denoted by \(H(1)\), is isomorphic to a subgroup of the group of all bijection map from \(G\) to \(G\) under composition of functions. Moreover, it is proved that \(H(1)\) is embedded in the group of all invertible linear operators on \(C(G)\), the set of all complex continuous function on \(G\).
ISSN:2331-8422